作为拉格朗日规范理论的Adler-Kostant-Symes系统
Adler-Kostant-Symes systems as Lagrangian gauge theories
摘要：
众所周知，由Adler-Kostant-Symes构造定义的可积Hamilton系统通过Hamilton约化对应于李群余切丛上的系统。推广以前的结果户田系统，在这里展出的拉格朗日版本的减少过程的情况下，基本李代数承认一个不变的标量积。这是通过构造一个具有规范对称性的拉格朗日量来实现的，通过狄拉克算法，这个拉格朗日量再现了阿德勒-科斯坦特-赛姆斯系统，其哈密顿量是与李代数上的标量积相关的二次形式。
英文摘要：
It is well known that the integrable Hamiltonian systems defined by the Adler-Kostant-Symes construction correspond via Hamiltonian reduction to systems on cotangent bundles of Lie groups. Generalizing previous results on Toda systems, here a Lagrangian version of the reduction procedure is exhibited for those cases for which the underlying Lie algebra admits an invariant scalar product. This is achieved by constructing a Lagrangian with gauge symmetry in such a way that, by means of the Dirac algorithm, this Lagrangian reproduces the Adler-Kostant-Symes system whose Hamiltonian is the quadratic form associated with the scalar product on the Lie algebra.
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